The minimal pointed Weierstrass equations are studied in [1]}.
For a given \((C, w_0)\) , the minimal pointed Weierstrass equation
exists and is unique up to the transformations described in Lemma REF 
below. See also [1]} and [3]}, Corollary 5.2.
The next lemma is stated in [1]}, Remark after Definition 2.1.
